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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 2, Pages 111–124 (Mi izv635)  

On the Brauer group of an algebraic variety over a finite field

T. V. Zasorina

Vladimir State University

Abstract: For an arithmetic model $X\to C$ of a smooth regular projective variety $V$ over a global field $k$ of positive characteristic, we prove the finiteness of the $l$-primary component of the group $\operatorname{Br}'(X)$ under the conditions that $l$ does not divide the order of the torsion group $[\operatorname{NS}(V)]_{tors}$ and the Tate conjecture on divisorial cohomology classes is true for $V$.

DOI: https://doi.org/10.4213/im635

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English version:
Izvestiya: Mathematics, 2005, 69:2, 331–343

Bibliographic databases:

UDC: 512.6
MSC: 11G35, 11R37, 11R42, 11S40, 11S80, 14C22, 14F22, 14J28, 14F22
Received: 16.03.2004

Citation: T. V. Zasorina, “On the Brauer group of an algebraic variety over a finite field”, Izv. RAN. Ser. Mat., 69:2 (2005), 111–124; Izv. Math., 69:2 (2005), 331–343

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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